The goal of this solicitation is to develop, conduct and analyze a randomized three-arm breast cancer prevention study among women age 40-50 years of age or <40 years if Gail risk ?1.66 (including BRCA1/2 mutation carriers) with mammographically dense breasts (BIRADS C or D, according to fifth edition classification) to assess whether daily application of 2 mL or 4 mL of afimoxifene (4-hydroxytamoxifen) gel lowers breast density.